Welcome to the Forum, John:
Water takes its good ol easy time to soak through the ground. In your case, yes, I do believe you had some frozen water in the ground which thawed out later and seeped on through. I would not consider a basement without a sump pump unless it had a walk-out side and natrual drainage from there. The price of the pump will be pennies compared to 2' of water in a finished basement. Let us know how it works out, and maybe a picture or two.